Once you have it, simply follow the trail until you find the wolf and its two companions. You’ll have a third mission slot by then, and the Moonstone wolf mission is one of the options that can appear there. The easiest way to get to the Legendary Moonstone Wolf is to bump up your naturalist level up to 12 and head over to Harriet.
If you’re in the right spot and the animal isn’t showing up, you should try joining another session.
Some legendary animals don’t spawn unless your naturalist rank is high enough, so keep doing those missions.
Your best bet for finding the legendary wolves is using the map and relying on missions from Harriet.